A parabola of latus rectum `l` touches a fixed equal parabola. The axes of two parabolas are parallel. Then find the locus of the vertex of the moving parabola.

If the focus of a parabola is (2, 3) and its latus rectum is 8, then find the locus of the vertex of the parabola.

Find the vertex of the parabola x^2=2(2x+y)

The vertex of the parabola x^(2)=8y-1 is :

The vertex of the parabola y^2 + 4x = 0 is

A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is :

Find the locus of the midpoint of normal chord of parabola y^2=4ax

Find the length of the Latus rectum of the parabola y^(2)=4ax .

A P is perpendicular to P B , where A is the vertex of the parabola y^2=4x and P is on the parabola. B is on the axis of the parabola. Then find the locus of the centroid of P A Bdot

If the vertex of the parabola is (3,2) and directrix is 3x+4y-(19)/7=0 , then find the focus of the parabola.